Aahhh... thanks for the explanation - I completely didn't recognize it as roman numerals, but it is so obvious now.(as with other puzzlr questions, it's interesting that there can be alternate explanations than was intended, ie the algebraic interpretation)

This is not an algebraic equation, these are Roman numerals. The Roman numeral X equals 10, the Roman numeral I equals 1. However, the way the numerals add up is dependent on their order. If the smaller numeral is after the larger one, their values are added together, so XI has a value of 11, whereas if you place the smaller numeral before the larger one, you subtract the smaller from the larger, meaning IX equals 9. So the original equation XI + I = X would mean 11 + 1 = 10 which is incorrect. The mirror image of that becomes X = I + IX which is 10 = 1 + 9 which is indeed true.

I may be drunk on chocolate, but I don't understand why the mirror/flip solution makes it 'correct'. the better answer on pzzlr is "(X=0, I=0) as well as (X=-2, I=2) would satisfy the equation or make it correct"